Explicit evaluation of some exponential sums
type: Item
instance of: scholarly article
title: Explicit evaluation of some exponential sums
zbMATH Open document ID: 1221.11234
published in: Finite Fields and their Applications
publication date: 2009-12-22T00:00:00Z
review text: Let \(m\) be a positive integer and let \(r\) be a prime such that 2 is a primitive root modulo \(r^m\). Set \(q=2^{\varphi (r^m)}\), \(\varphi\) the Euler function, and let \(\chi\) be the canonical additive character of \(\mathbb F_q\). For \(a,b\in \mathbb F_q\), the exponential sum \[ S(a,b)=\sum_{x\in\mathbb F_q^*} \chi (ax^{(q-1)/r^m}+bx) \] is evaluated. The answer is in terms of the Hamming weights of subvectors of a certain coordinate vector of \(ab^{-(q-1)/r^m}\). This is applied to the weight distribution of the dual of a binary cyclic code.
Mathematics Subject Classification ID: 11T23
Mathematics Subject Classification ID: 11L03
Mathematics Subject Classification ID: 11T71
Mathematics Subject Classification ID: 94B15
zbMATH DE Number: 5651168
zbMATH Keywords: cyclic code
zbMATH Keywords: exponential sum
zbMATH Keywords: weight distribution
author: Marko Moisio
MaRDI profile type: Publication
full work available at URL: j.ffa.2009.05.005
OpenAlex ID: W1997600827
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DOI: 10.1016/J.FFA.2009.05.005
description: scientific article; zbMATH DE number 5651168